An important function that must be provided in optical networks is wavelength routing. In particular, wavelength routing is needed at each node, in order to combine and separate different wavelength channels. Typically, the router is realized in integrated form by using a waveguide grating, and an example is shown in FIG. 1. The router in this example only includes one input waveguide and its purpose is to separate the input channels, and transmit them to different output waveguides. The waveguide grating simply transforms each input signal, intended for a particular output waveguide, into a corresponding output image produced (approximately) at the output waveguide location. However, an undesirable feature of this router is its narrow bandwidth, caused by the strong wavelength dependence of each image location produced by the grating. Because of this variation, maximum transmission to each output waveguide is only realized in the immediate vicinity of the center wavelength of maximum transmission for that waveguide.
In order to solve this problem, one must use a planar arrangement of two gratings of opposite dispersions as shown previously in U.S. Pat. No. 5,488,680 which issued on Jan. 30, 1996, U.S. Pat. No. 7,043,123 B2 which issued on May 9, 2006, and U.S. Pat. No. 7,283,700 B2 Oct. 16, 2007. By this technique, the router produces, at the location of each output waveguide, a stationary image producing a maximally flat transmission coefficient. However, an undesirable feature of both patents is the large size of the router. In particular, the second patent requires between the two gratings several waveguide lenses, one for each output waveguide and, as a consequence, this arrangement is only feasible if the number of lenses is small. As shown in FIG. 3 this arrangement consists of two stages 311 and 312 (two waveguide gratings) interconnected by a set 313 of N waveguide lenses 328. The waveguide lenses are connected between the focal circles 323 and 324 of the two stages. On the output focal circle 324, the N lenses are separated by small gaps, thus producing N separate images, respectively transmitted to the N output waveguides 308. By using this technique, a 1×5 router was demonstrated with excellent results. However, an undesirable feature of this router is the large size of each stage. This is partly caused by the large number of waveguides (typically about 10) in each lens, resulting in a large increase in number of arms in each grating, by at least a factor of 3 as compared to a conventional waveguide grating router (shown in FIG. 1). Moreover, the router of FIG. 3 only includes one input waveguide and, as shown later, it is not periodic. Accordingly, here both size and performance are substantially improved, and a new M×N router featuring increased number of passbands and improved performance is described.